Tiao Lu

Tiao Lu
Peking University | PKU · School of Mathematical Sciences

Ph. D.

About

46
Publications
3,022
Reads
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582
Citations
Additional affiliations
August 2006 - present
Peking University
Position
  • Professor (Associate)
August 2004 - August 2006
University of North Carolina at Charlotte
Position
  • Visiting Assistant Professor

Publications

Publications (46)
Article
Full-text available
The historical analysis demonstrates that plasma scientists produced a variety of numerical methods for solving “kinetic” models, i.e., the Vlasov-Maxwell (VM) system. Still, on the other hand, a significant fact or drawback of most algorithms is that they do not preserve conservation philosophies. This is a crucial fact that cannot be disregarded...
Article
In this study, we design a specific geometry of plasma particles and further translate it into mathematical form, i.e., formulated time-fractional semi relativistic Vlasov Maxwell system. This extended version of model is very significant and ground-breaking because it has ability to study the behavior of plasma particles at macroscopic and microsc...
Article
Purpose The purpose of this offered research is to articulate a multifaceted kind of highly unstable initial perturbation and further analyze the performance of the plasma particles for time-fractional order evaluation. Design/methodology/approach For this purpose, the authors designed specific geometry and further interpreted it into the mathemat...
Article
With the historical review, it can determine that plasma scientists devolved many numerical schemes in literature to solve the kinetic plasma models such as Vlasov- Maxwell system, but the fatal problem is that most of the designed algorithms violate the conservation laws. This issue is significant and cannot disregard because the Vlasov Maxwell sy...
Article
The “Vlasov-Maxwell system” is a groundbreaking algorithm to model, simulate and further analyze the vigorous performance of the collisionless plasma in the presence of the electromagnetic fields. In this frame of reference, the inquiry of this system with the deep conceptions of the time-fractional derivative is a novel benchmark and also the key...
Article
Full-text available
The “Vlasov-Maxwell system” is a groundbreaking differential procedure to visualize, model, simulate and further analyze the vigorous performance of plasma (collisionless) in the presence of the different fields (electromagnetic). In this frame of reference, the analysis of “Vlasov-Maxwell system” with the deep conceptions of (time-fractional) calc...
Article
The Vlasov–Maxwell system is a revolutionary tool to model and analyze the dynamic behavior of the collisionless plasma in the existence of the electromagnetic field. In this perspective, the investigation of this system with the concept of the time‐fractional derivative is the new benchmark and also one of the main objectives of this article. To c...
Article
Full-text available
The stationary Wigner inflow boundary value problem (SWIBVP) is modeled as an optimization problem by using the idea of shooting method in this paper. To remove the singularity at \(v=0\), we consider a regularized SWIBVP, where a regularization constraint is considered along with the original SWIBVP, and a modified optimization problem is establis...
Article
Full-text available
In Li et al. (J Sci Comput 62:317–335, 2015), we thoroughly investigated the structure of the kernel space of the discrete one-dimensional (1D) non-polar optical phonon (NPOP)-electron scattering matrix, and proposed a strategy to setup grid points so that the uniqueness of the discrete scattering kernel is preserved. In this paper, we extend the a...
Article
This paper proposes a systematic procedure to calibrate the parameters of the drift-diffusion (DD) model for a performance evaluation of InGaAs MOSFETs in the quasi-ballistic regime. The simulation results of a deterministic multi-subband Boltzmann transport equation (BTE) solver serve as the standard. The DD model is calibrated both under low and...
Article
Full-text available
In this work, the abstract Cauchy problem for an initial value system with singular integral is considered. The system is of closed form of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banach space, we prove the existence and uniqueness of classical solutions to the evolution system...
Article
A deterministic time-dependent Boltzmann transport equation (BTE) solver is employed to carry out a comparison work among 10 nm double-gate n-type MOSFETs with channel materials of Si, In0.53Ga0.47As, and GaSb in different surface orientations. Results show that the GaSb device has the highest drive current, while scattering affects carrier transpo...
Article
Full-text available
The performance of double gate GaSb nMOSFETs with surface orientations of (100) and (111) are compared by deterministically solving the time-dependent Boltzmann transport equation (BTE). Results show that the on-state current of the device with (111) surface orientation is almost three times larger than the (100) case due to the higher injection ve...
Article
For the stationary Wigner equation with inflow boundary conditions, its numerical convergence with respect to the velocity mesh size are deteriorated due to the singularity at velocity zero. In this paper, using the fact that the solution of the stationary Wigner equation is subject to an algebraic constraint, we prove that the Wigner equation can...
Article
We study the stationary Wigner equation on a bounded, one-dimensional spatial domain with inflow boundary conditions by using the parity decomposition in (Barletti and weifel, Trans. Theory Stat. Phys., 507--520, 2001). The decomposition reduces the half-range, two-point boundary value problem into two decoupled initial value problems of the even p...
Article
Full-text available
In this work, the transient characteristics of nanoscale field-effect transistors (FETs) have been investigated using a deterministic solver based on the time-dependent multi-subband Boltzmann transport equation (BTE). The response to a step signal superimposed on the gate or drain electrode is simulated. The transient process can be understood as...
Conference Paper
We investigate the scattering mechanism in ultrashort double gate In 0.53 Ga 0.47 As nMOSFETs by deterministically solving Boltzmann transport equation (BTE). The intra-valley acoustic phonon scattering, optical phonon scattering, intervalley optical scattering, polar optical scattering, and surface roughness (SR) scattering are considered. The imp...
Conference Paper
A nano-scale double gate In0.53Ga0.47As nMOSFET device structure is simulated by deterministically solving the time dependent Boltzmann Transport Equation (BTE). The results show that the contribution of the L valleys cannot be ignored even if the energy gap between r and L valleys are very large. Moreover, the quasi-ballistic transport is observed...
Article
We investigate the discretization of of an electron–optical phonon scattering using a finite volume method. The discretization is conservative in mass and is essentially based on an energy point of view. This results in a discrete scattering system with elegant mathematical features, which are fully clarified. Precisely the discrete scattering matr...
Article
The transient response to the drain voltage of a nano scale Ultra-Thin Body and BOX (UTBB) nMOSFET are investigated by deterministically solving the time dependent Boltzmann Transport Equation (BTE). The relaxation process of subbands profile, electron density and current is investigated. The relaxation time of the device is about 0.1ps at typical...
Article
Full-text available
Making use of the Whittaker-Shannon interpolation formula with shifted sampling points, we propose in this paper a well-posed semi-discretization of the stationary Wigner equation with inflow BCs. The convergence of the solutions of the discrete problem to the continuous problem is then analysed, providing certain regularity of the solution of the...
Article
Full-text available
We apply the Monte Carlo, stochastic Galerkin, and stochastic collocation methods to solving the drift-diffusion equations coupled with the Poisson equation arising in semiconductor devices with random rough surfaces. Instead of dividing the rough surface into slices, we use stochastic mapping to transform the original deterministic equations in a...
Article
Full-text available
By the moment closure of the Boltzmann transport equation, the extended hydrodynamic models for electron transport have been derived in Cai et al. (J Math Phys 53:103503, 2012). With the numerical scheme developed in Li et al. (2012) recently, it has been demonstrated that the derived extended hydrodynamic models can capture the major features of t...
Article
In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi-Dirac...
Article
Full-text available
Based on the well-posedness of the stationary Wigner equation with inflow boundary conditions given in (A. Arnold, H et al. J. Math. Phys., 41, 2000), we prove without any additional prerequisite conditions that the solution of the Wigner equation with symmetric potential and inflow boundary conditions will be symmetric. This improve the result in...
Conference Paper
The impact of back biasing on electron transport in extreme short channel Ultra-Thin Body and BOX (UTBB) SOI MOSFETs is investigated by a deterministic multi-subband Boltzmann solver. A 7.5nm channel length UTBB device is simulated, and its transport details are presented in this paper.
Conference Paper
A globally hyperbolic high-order moment method of the Boltzmann transport equation (BTE) is proposed in [1], [2], and here it is extended for the BTE with the electron-phonon scattering term to simulate a silicon nano-wire (SNW). Convergence with respect to the order of the moment system and the characteristics of SNW including the I-V curve are st...
Article
In the first of a series of papers, we will study a discontinuous Galerkin (DG) framework for many electron quantum systems. The salient feature of this framework is the flexibility of using hybrid physics-based local orbitals and accuracy-guaranteed piecewise polynomial basis in representing the Hamiltonian of the many body system. Such a flexibil...
Article
Full-text available
In this paper, we extend the method in Cai et al. (J Math Phys 53:103503, 2012) to derive a class of quantum hydrodynamic models for the density-functional theory (DFT). The most popular implement of DFT is the Kohn–Sham equation, which transforms a many-particle interacting system into a fictitious non-interacting one-particle system. The Kohn–Sha...
Article
In this study, we simulate double-gate MOSFET using a 2-D direct Boltzmann transport equation solver. Simulation results are interpreted by quasi-ballistic theory. It is found that the relation between average carrier velocity at virtual source and back-scattering coefficient needs to be modified due to the oversimplified approximations of the orig...
Article
Full-text available
A globally hyperbolic moment system upto arbitrary order for the Wigner equation was derived in [6]. For numerically solving the high order hyperbolic moment system therein, we in this paper develop a preliminary numerical method for this system following the NRxx method recently proposed in [8], to validate the moment system of the Wigner equation...
Article
Full-text available
In this paper, we derive the quantum hydrodynamics models based on the moment closure of the Wigner equation. The moment expansion adopted is of the Grad type firstly proposed in \cite{Grad}. The Grad's moment method was originally developed for the Boltzmann equation. In \cite{Fan_new}, a regularization method for the Grad's moment system of the B...
Conference Paper
Quasi-ballistic asymmetric DG-MOSFET has been simulated using a multi-subband Boltzmann transport equation solver and important parameters regarding to back-scattering at the top of barrier are carefully studied in this work. It is observed that the simulated results are in good agreement with established theory and phonon scattering still plays an...
Article
In this paper, the ballistic and quasi-ballistic transport characteristics of Sub-30 nm double gate MOSFETs are simulated by deterministic solver of the Time Dependent Muti-subbands Boltzmann Transport Equation [1]. The scattering effect on the Sub-30 nm double gate MOSFETs is investigated not only through analyzing ON current, but also the source...
Article
Full-text available
A new adaptive cell average spectral element method (SEM) is proposed to solve the time-dependent Wigner equation for transport in quantum devices. The proposed cell average SEM allows adaptive non-uniform meshes in phase spaces to reduce the high-dimensional computational cost of Wigner functions while preserving exactly the mass conservation for...
Article
Full-text available
We propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation (MSBTE) for the two dimensional (2D) electron gas in double gate metal oxide semiconductor field effect transistors (MOSFETs) with flared out source/drain contacts. A realistic model with six-valleys of the conduction band of silicon and both intra-v...
Article
Full-text available
As MOSFETs scaling down to nano-scale, short channel effect(SCE) become a critical issue. Multiple channel MOSFET structure such as FINFET has well gate controllability on channel charge, and will be used in nano-scale CMOS technology. In this work the performance of 20nm bulk FINFET is investigated by Using 3D full band Monte Carlo Method with Eff...
Conference Paper
Full-text available
The lattice scattering is carefully involved in a direct solution of the BTE and Poisson-Schrodinger equation method. Simulating results of a 9 nm DG MOSFET shows the lattice scattering effects on the barrier height and the positions of barrier peak are small, but the effects on the carrier drift velocity are strongly. Not only intra-valley scatter...
Article
To enhance the accuracy of three-dimensional geological model, emphasize the high local relevance characteristics of the complex geological bodies, and avoid complicated calculation and dependence on human experience in traditional interpolation methods, the natural neighbor interpolation (NNI) method was used for three-dimensional discrete data in...
Conference Paper
Full-text available
We present a self-consistent multi subband deterministic solver of the Boltzmann transport equation of the two dimensional (2D) electron gas. The Schodinger equation at each slice in the confinement direction and the two dimensional Poisson equation are self-consistently solved with the Boltzmann transport equation. The energy quantization and the...
Article
In this paper, we propose a high order Fourier spectral-discontinuous Galerkin method for time-dependent Schrödinger–Poisson equations in 3-D spaces. The Fourier spectral Galerkin method is used for the two periodic transverse directions and a high order discontinuous Galerkin method for the longitudinal propagation direction. Such a combination re...
Article
Full-text available
This paper presents the study of coupling efficiencies between two-dimensional (2-D) waveguides and microring resonators with a newly developed high-order discontinuous Galerkin time domain (DGTD) method for Maxwell's equations. The DGTD method is based on a unified formulation for the physical media and the artificial media in the uniaxial perfect...
Article
Full-text available
This paper presents a newly developed high-order discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations in linear dispersive media with UPML boundary treatment. A unified formulation is derived for linear dispersive media of Debye type and the artificial material in the UPML regions with the help of auxiliary differential...
Article
This paper presents a high order local discontinuous Galerkin time-domain method for solving time dependent Schrodinger equations. After rewriting the Schrodinger equation in terms of a flrst order system of equations, a numerical ∞ux is constructed to preserve the conservative property for the density of the particle described. Numerical results f...
Article
In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwell's equations in linear dispersive and lossy materials of Debye type and in the artificial perfectly matched layer (PML) regions. An auxiliary differential equation (ADE) method is used to handle the frequency-dependent constitutive relations with...

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Project (1)
Project
numerical methods and theoretical analysis